Chords AB and CD of a circle, when produced, meet at a point P outside the circle. If AB = 6 cm, CD = 3 cm and PD = 5 cm, then PB is equal to:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 4 cm.
According to the given question,
In the above figure, PA × PB = PC × PD
Also, PA = (6 + x) cm
⇒ (6 + x) × x = 8 × 5
⇒ x2 + 6x - 40 = 0
⇒ x2 + 10x - 4x - 40 = 0
⇒ x(x + 10) - 4(x + 10)
⇒ (x - 4)(x + 10) = 0
⇒ x = 4; x = -10 (Not possible)
Hence, PB = 4 cm